Basic scientific achievements

The main scientific direction is devoted to the study of the embedding theorem to functional spaces. In other words, new Morrey spaces with new parameters are introduced. To study the differential and differential-difference properties of functions from these spaces, both integrable and interpolated theorems are proved using the integral representation. It is also proved that the generalized mixed derivative of the functions from these spaces belong to the Hölder class. It should be noted that in the parametric case, representations of smoothness index is higher than in the case of the classical representation are proved. The obtained theoretical results are effectively applied to the problems of existence, uniqueness, and solvability of solutions of the corresponding partial differential equations. In other words, the high degree of the smoothness index of the considered generalized solutions of equations approximates it even closer to the case of the classical solution.

The list of publications at the 5 years published

1. On Riesz-Thorin type theorems in Besov-Morrey spaces and its applications, American Journal of Mathematics and Mathematical Sciences vol.1, No.2, 2012,pp.139-154.(həmməllif A.M.Najafov).
2. On properties of generalized spaces Besov – Morrey, with dominant mixed derivatives, Proceeding of Institute of Mathematics and Mechanics, vol. 41, №1. Pp.3-15. Baku-2015 (həmməllif A.M.Najafov).
3. Interpolation theorems of the generalized Besov- Morrey type spaces with dominant mixed derivatives, Transactions of NAS of Azerbaijan, Issue Mathematics, 35 (4), 131-142 (2015).
4. On solutions of one class of partial differential equations, Electron. Jour. Qual. Theory Differ. Equ. 2017, No. 44, 1-9. IF.0,926 (Q1)TR https://doi.org/10.14232/ejqtde.2017.1.44 (həmməllif A.M.Najafov).
5. Interpolation theorems on the Nikolskii-Morrey type spaces, Caspian Journal of Applied Mathematics, Ecology and Economics, 6(1) July,2018, pp-111-121.(həmmüəllif Mustafayeva F.F.)
6. On embedding theorems in Sobolev-Morrey type spaces Journal of Contemporary Applied Mathematics, Vol. 8, no2, 2018, http://journalcam.com/wp-content/uploads/2018/09/2.pdf (həmmüəllif R.F. Babayev)